A glass capillary tube is of the shape of a truncated cone with an apex angle `alpha` so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a high h, where the radius of its cross section is b. If the surface tension of water is S, its density if `rho`, and its contact angle with glass is `theta`, the value of h will be (g is the acceleration due to gravity)

Options

A. `(2S)/(brhog)cos(theta-alpha)`
B. `(2S)/(brhog)cos(theta+alpha)`
C. `(2S)/(brhog)cos(theta-(alpha)/(2))`
D. `(2S)/(brhog)cos(theta+(alpha)/(2))`

Answer

D

Explanation

`(b)/(R)=cos(theta+(alpha)/(2))`
Using pressure equation along the path MNTK
`p_(0)-(2S)/(R)+hrhog=p_(0)`